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Mirrors > Home > HSE Home > Th. List > df-bdop | Structured version Visualization version GIF version |
Description: Define the set of bounded linear Hilbert space operators. (See df-hosum 29509 for definition of operator.) (Contributed by NM, 18-Jan-2006.) (New usage is discouraged.) |
Ref | Expression |
---|---|
df-bdop | ⊢ BndLinOp = {𝑡 ∈ LinOp ∣ (normop‘𝑡) < +∞} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbo 28727 | . 2 class BndLinOp | |
2 | vt | . . . . . 6 setvar 𝑡 | |
3 | 2 | cv 1536 | . . . . 5 class 𝑡 |
4 | cnop 28724 | . . . . 5 class normop | |
5 | 3, 4 | cfv 6357 | . . . 4 class (normop‘𝑡) |
6 | cpnf 10674 | . . . 4 class +∞ | |
7 | clt 10677 | . . . 4 class < | |
8 | 5, 6, 7 | wbr 5068 | . . 3 wff (normop‘𝑡) < +∞ |
9 | clo 28726 | . . 3 class LinOp | |
10 | 8, 2, 9 | crab 3144 | . 2 class {𝑡 ∈ LinOp ∣ (normop‘𝑡) < +∞} |
11 | 1, 10 | wceq 1537 | 1 wff BndLinOp = {𝑡 ∈ LinOp ∣ (normop‘𝑡) < +∞} |
Colors of variables: wff setvar class |
This definition is referenced by: elbdop 29639 hhbloi 29681 |
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